Lightmap overlapping error when importing to UE4
It looks like you have overlapping areas in the packed UV map. You can see these long diagonal streaks going in your layouts that intersect other UV faces. But it's hard to tell what's going on there without seeing the .blend.

One pointer is if you use N-gons in modeling make sure to convert them to quads and tris before using pack in UV editor because it seems to often screw the N-gons. You can find N-gons be selecting a quad face and finding faces with more polygon sides with SHIFT+G. You can triangulate them with CTRL+T and join back to quads what you can with ALT+J.

Smart UV project (also includes packing algorithm that seems to work) handles them fine, as well as unwrap and I guess it won't be long until pack itself will be fixed to handle them properly. I recommend just using the smart UV project (if you don't want to manually unwrap with seams that yields best results) to pack all of the object at once and generally making your levels out of smaller rather than larger sets of geometry.

Also please use margin around your islands. When the lightmaps are baked if you have light and dark areas very close to each other in the map they are going to bleed into eachothers areas as the map is sampled.